Yasir Shah celebrates taking the wicket of Dom Sibley at Ageas Bowl cricket stadium on Friday. Reuters
Crawley brought up an 80-ball fifty off the last ball of the session when, tempted to drive after Pakistan reinforced the slip cordon, he stylishly struck Shaheen Afridi down the ground to long-off for the seventh four of his innings.
England captain Joe Root, who won the toss, was 10 not out.
Root, with England needing to avoid defeat to secure a first series win over Pakistan in a decade at 1-0 up in a three-match campaign, decided to bat on a blustery morning where the sun was starting to break through the clouds.
England suffered an early setback when Rory Burns, in a tough series for openers, nicked a full-length delivery from fellow left-hander Afridi that moved away late, with Shan Masood holding a good low catch at fourth slip.
Burns stood his ground but replays confirmed it was a fair catch and he was out for six, the batsman now averaging a lowly five from four innings this series.
Crawley, fresh from his 53 in the second innings of the drawn second Test at Southampton, cut leg-spinner Yasir Shah for four and glanced paceman Naseem for another boundary.
And when Naseem was fractionally short, Crawley pulled him for a resounding four well in front of square.
Yasir gets Sibley
But a second-wicket stand worth of 61 ended when Dom Sibley, going down the pitch to Yasir, was given out lbw for 22 following an impassioned appeal by the bowler.
Sibley reviewed but one of the lessons of this season is that a challenge to a decision by umpire Michael Gough rarely succeeds and, with tracking technology indicating the ball would have hit middle stump, England were 73-2.
Crawley then spent several deliveries stuck on 49 in the face of accurate Pakistan bowling before his patience was rewarded with a deserved fifty.
England made just one change following the second Test, a match marred by weather delays, with fast bowler Jofra Archer replacing Sam Curran.
Left-arm seamer Curran had been brought into the side in place of Ben Stokes, with the star all-rounder missing the last two Tests of the series to be with his ill father in New Zealand.
"When Sam plays it obviously improves the batting, but we feel we've got the strength," Root told Sky Sports after winning the toss.
"Jofra has had a week off. We want him to operate in short and sharp spells and we want him to bowl fast."
Pakistan were unchanged, with captain Azhar Ali saying: "It's a very important Test match for us. We want to give everything in this game."
This match marked the last of six scheduled Tests in the English season, which have all been played behind closed doors because of the coronavirus outbreak, with England defeating the West Indies 2-1 last month.
England are now set to play all of their planned 18 internationals, across all formats this season, despite the COVID-19 crisis.
Following the delays in the second Test, this match will see play allowed to start half an hour earlier than the scheduled 11:00am (1000 GMT) in a bid to make up for any overs lost to bad light.
Pakistan were dismissed for 273, a huge 310 runs behind England's imposing 583-8 declared, on the third day of the third Test.
Pakistan were 223-9 at stumps on the second day, with Rizwan 60 not out just as he started to up the tempo of his innings with only last man Naseem Shah for company.
Shaheen Afridi needed just four balls to remove England's Rory Burns for a duck on Sunday before bad weather again interrupted the second Test at Southampton. England were 7-1 in reply to Pakistan's first innings 236 when rain stopped play at 12:00pm local time on the fourth day.
Only 134.3 overs were possible in the entire match, which included a 38 over spell late on the fifth afternoon as the sun finally came out, with England finishing on 110 for four before the game was called off with no prospect of a winner.
Chinese trampoline gymnast Dong Dong narrowly missed out on gold at the Tokyo Olympics on Saturday but became the first athlete in the sport to win four medals at four Games.
Weightlifter Fares ElBakh shattered two Games records in Tokyo as he became Qatar’s first Olympic champion in history on Saturday.
Patiala-born 25-year-old Indian discus thrower Kamalpreet Kaur came up with a scintillating performance to secure her place in the final at the Tokyo Olympic Games